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Abstract
A BH(q,n) Butsontype Hadamard matrix H is an n×n matrix over the complex qth roots of unity that fulfils HH^{∗}=nI_{n}. It is well known that a BH(4,n) matrix can be used to construct a BH(2,2n) matrix, that is, a real Hadamard matrix. This method is here generalised to construct a BH(q,pn) matrix from a BH(pq,n) matrix, where q has at most two distinct prime divisors, one of them being p. Moreover, an algorithm for finding the domain of the mapping from its codomain in the case p=q=2 is developed and used to classify the BH(4,16) matrices from a classification of the BH(2,32) matrices.
Original language  English 

Pages (fromto)  23872397 
Number of pages  11 
Journal  Discrete Mathematics 
Volume  341 
Issue number  9 
DOIs  
Publication status  Published  1 Sep 2018 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Butsontype Hadamard matrix
 Classification
 Complex matrix
 Mapping
 Monomial equivalence
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 1 Finished

Construction and Classification of Discrete Mathematic Structures
Kokkala, J., Laaksonen, A., Östergård, P., Szollosi, F., Pöllänen, A., Heinlein, D. & Ganzhinov, M.
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding